“This is an ongoing investigation so it would not be appropriate to comment further, but the Prime Minister believes that child abuse imagery is abhorrent and that anyone involved with it should be properly dealt with under the law”.

Rock, who helped draw up guidelines on internet porn filters, was an adviser to the Conservative party for 30 years.

A friend of Cameron told the Daily Mail, which uncovered the arrest, that the prime minister was “extremely shocked”.

“Downing Street confirmed Rock was one of the advisers involved in the Government’s policy on internet filters to protect against child abuse images online.

Google and Microsoft agreed in November to introduce changes that will prevent such images from being listed in results for more than 100,000 searches.

A Downing Street spokeswoman said: “Patrick Rock was one of a number of advisers and officials involved in dealing with this issue but the work was led by somebody else, and decisions were taken by ministers.”

An NCA spokeswoman declined to comment, stating it did not name suspects on arrest.